In this paper, the existence and exponential stability of anti-periodic solutions for Shunting Inhibitory Cellular Neural Networks (SICNNs) with continuously distributed delays are considered by constructing suitable Lyapunov fuctions and applying some critical analysis techniques. The authors' result remove restrictive conditions of the global Lipschitz and bounded conditions of activation functions and new sufficient conditions ensuring the existence and exponential stability of anti-periodic solutions for SICNNs are obtained. Moreover, an example is given to illustrate the feasibility of the conditions in their results.